算法梳理进阶线性回归(二)

拼搏现实的明天。 2022-03-15 11:14 191阅读 0赞

### 文章目录 ###

上次简单介绍了线性回归原理以及公式推导，今天用python代码简单实现下单变量线性回归：

# -*- coding:utf-8 -*-
    import numpy as np
    from matplotlib import pylab as pl
    
    
    class LRArithmetic:
    
        def __init__(self, x, y):
            """
            Parameters of the loading
            :param x:
            :param y:
            """
            self.x = np.array(x)
            self.y = np.array(y)
    
            # Check data
            if len(x) != len(y):
                raise ValueError('There is a problem with the input data!!!')
    
            # Initialize the parameters of the unary equation: y = wx + b
            self.w = 0
            self.b = 0
            self.is_fit = False
    
        def fit_arithmetic(self):
            """
             Calculate the parameters of w and b by arithmetic method
            :return:
            """
            # Calculate the mean of x and y
            x_mean = np.mean(self.x)
            y_mean = np.mean(self.y)
    
            # Calculate the numerator and denominator
            numerator = 0
            denominator = 0
            for i in range(len(self.x)):
                numerator += (self.x[i] - x_mean) * (self.y[i] - y_mean)
                denominator += np.square((self.x[i] - x_mean))
            self.w = numerator / denominator
            self.b = y_mean - self.w * x_mean
            self.is_fit = True
    
        def fit_vector(self):
            """
            Calculate the parameters of w and b by vector method
           :return:
           """
            # Calculate the mean of x and y
            x_mean = np.mean(self.x)
            y_mean = np.mean(self.y)
    
            # Calculate the numerator and denominator
            numerator = np.sum((self.x - x_mean) * (self.y - y_mean))
            denominator = np.sum(np.square(self.x - x_mean))
    
            self.w = numerator / denominator
            self.b = y_mean - self.w * x_mean
            self.is_fit = True
    
        def predit(self, x):
            """
            Predicted data
            :param x:
            :return:
            """
            if not self.is_fit:
                raise RuntimeError('Please call the fit method first!!!')
            return np.array(x) * self.w + self.b
    
    
    if __name__ == '__main__':
        # train
        x = np.array([1, 3, 2, 1, 3])
        y = np.array([14, 24, 18, 17, 27])
        LR = LRArithmetic(x, y)
        LR.fit_vector()
    
        # predit
        x_test = np.array([2, 3, 5, 6, 10])
        y_test = LR.predit(x_test)
        print(y_test)
    
        xx = np.linspace(0, max(x_test))
        yy = LR.w * xx + LR.b
        pl.plot(xx, yy, 'k-')
        pl.scatter(x, y, cmap=pl.cm.Paired)
        pl.scatter(x_test, y_test, cmap=pl.cm.Paired)
        pl.show()

运行效果如下图：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM2NzExMjg5_size_16_color_FFFFFF_t_70]  
注： 蓝色的是训练数据，橙色的是预测的结果  
使用fit\_vector向量计算方法进行训练对比fit\_arithmetic循环方式，数据量少时看不出太大的时间差，不过向量方式计算在性能上肯定是原因比循环要快的。推荐使用numpy和pandas下的包来进行计算，毕竟做过优化。

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM2NzExMjg5_size_16_color_FFFFFF_t_70]: /images/20220315/b11eeef7c3654e0ea45b6ae7322d8522.png